As a matter of fact the charge \(Q\)  is precisely also the conserved Noether charge associated to the U(1) duality symmetry of the NLE theory and
of its Hamiltonian action \(S^{(1)}_{RS}[\Phi ^\mu ,{\Phi ^\mu }^*]\) , and the generator of that symmetry[1]}, [2]}.
On account of Noether's first theorem[3]} it may readily
be established that the corresponding conserved spacetime covariant Noether current density is simply given by
\(J^\mu _{\rm dual}=\frac{1}{2}\left(J^\mu +{J^\mu }^*\right),\qquad \partial _\mu J^\mu _{\rm dual}=0,\) 
